Multiple–test procedures and smile plots

Roger Newson
King's College London, UK
roger.newson@kcl.ac.uk

The ALSPAC Study Team
University of Bristol, UK
http://www.alspac.bris.ac.uk

Abstract.multproc carries out multiple-test procedures, taking as input a list
of p-values and an uncorrected critical p-value, and
calculating a corrected overall critical p-value for rejection of null
hypotheses. These procedures define a confidence region for a set-valued
parameter, namely the set of null hypotheses that are true. They aim to
control either the family-wise error rate (FWER) or the false discovery rate
(FDR) at a level no greater than the uncorrected critical p-value.
smileplot calls multproc and then creates a smile plot, with
data points corresponding to estimated parameters, the p-values (on a
reverse log scale) on the y-axis, and the parameter estimates (or
another variable) on the x-axis. There are y-axis reference
lines at the uncorrected and corrected overall critical p-values. The
reference line for the corrected overall critical p-value, known as
the parapet line, is an informal “upper confidence limit” for
the set of null hypotheses that are true and defines a boundary between data
mining and data dredging. A smile plot summarizes a set of multiple
analyses just as a Cochrane forest plot summarizes a meta-analysis.